Puzzler: The farmer and the 40 lb stone (10/22/11) (NO ANSWER GIVEN)

The Puzzle of Oct 22, 2011: A farmer has a 40 lb stone that he uses to measure out bales of hay on a 2 sided balance. He loans it to a friend who accidentally breaks it into 4 pieces. Instead of being angry, the farmer is quite happy. He says to the friend, "You managed to break it into just the right 4 pieces that will now let me weigh any weight between 1 and 40." What are the weights of the 4 pieces?

I propose a second challenge: Are there any posters out there with black belts in Google who can find the solution on the internet? The solution is out there.

Maybe because it's a reused puzzler. Good title by the way. I hope anyone who wants to discuss possible solutions will start a new topic for that. I'm waiting for them to post the transcript so I can re"hear" the puzzler... streaming other stuff now.

MikeInNH — "No...it's probably because cartalk is the only thing google can find on the subject."

Not true. The Google quest must be properly phrased to return a solution.

MikeInNH — "Here's a hint....Hopefully it won't give it away."

That is not a hint at all, because one would still be left in choosing, presumably at random, four weights that could be placed on a balance scale to balance any integer weight between 1 and 40 lbs.Warning! Hint given below.

Proceed more methodically. Find the smallest stone, of weight W(2) lbs, that can be broken into two parts, such that the two smaller broken pieces can balance any weight from 1 to W(2) lbs. Then proceed to find the next smallest weight, W(3) lbs, that can be broken in to three pieces, etc. ... and proceed in that fashion to find the smallest weight, W(n) lbs, that can be broken into n pieces that can be used to balance any weight from 1 to W(n) lbs. (Obviously, W(4) = 40 lbs.) By solving initially the n=2 problem, a general solution will emerge.